INSTRUCTIONS
Once the applet has finished loading, a "Lab-value" buttonwill appear
on the screen. This may take a minute or two depending on the speed of
your internet connection and computer. Please be patient. If no begin button
appears, it is probably because your browser does not support Java 1.1.
The Z statistic is used for inference procedures on the population mean. In this lab, because the null hypothesis Ho: mu=muo is true, then the value of the mean mu is equal to the hypothesized value muo. Therefore, in the Z statistic, we can replace mu by its value muo, yielding the Z test statistic
Z=(XBar-muo)/(sigma/square root n)
In the "Sampling Distributions" Lab, we learned that the Z statistic has a standard normal distribution if the parent population belongs to the family of normal distribution. If the parent population is not normally distributed, then the Central Limit Theorem ensures the sampling distribution of Z can still be well approximated by a standard normal distribution if the sample size is large enough. Throughout our tour of the Level of Significance of a Test Lab, we are going to learn how the validity of these statements affects the actual propotion of samples that will result in a value of Z that rejects the null hypothesis and compare that proportion to the desired value of alpha(the level of a significance of a test).
Press the "Lab-value" button, choice which parent population you want "Sample from", choice how many times you want "Repeat", then "Run" the lab. You use "Repeat" button to cumulate your repeat values.
There will be a table show the comparation from the percentiles of the theoretical normal distribution to the histogram. The first column of numbers (which includes 2.5, 5.0..., 97.5) are areas to the left of the numbers in the second column for the theoretical(standard normal) distribution. The third column of numbers are percentiles from the histogram. The numbers in the fourth column are the areas from the histogram to the left of the percentiles in the second column.